PHP Class MathPHP\Probability\Distribution\Continuous\Continuous

Inheritance: extends MathPHP\Probability\Distribution\Distribution

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Public Methods

Method	Description
above ( number $x, $params ) : number	CDF above - Probability of being above x to ∞ Area under a continuous distribution, that lies above a specified point.
between ( number $x₁, number $x₂, $params ) : number	CDF between - probability of being between two points, x₁ and x₂ The area under a continuous distribution, that lies between two specified points.
inverse ( number $target, $params )	The Inverse CDF of the distribution
outside ( number $x₁, number $x₂, $params ) : number	CDF outside - Probability of being below x₁ and above x₂.
rand ( $params )	Produce a random number with a particular distribution

P(above) = 1 - CDF(x)

public static above ( number $x, $params ) : number
$x	number
$params		Remaining parameters for each distribution
return	number

P(between) = CDF($x₂) - CDF($x₁)

public static between ( number $x₁, number $x₂, $params ) : number
$x₁	number	Lower bound
$x₂	number	Upper bound
$params		Remaining parameters for each distribution
return	number

For example, if the calling class CDF definition is CDF($x, $d1, $d2) than the inverse is called as inverse($target, $d1, $d2)

public static inverse ( number $target, $params )
$target	number	The area for which we are trying to find the $x
$params		List of all the parameters that are needed for the CDF of the calling class. This list must be absent the $x parameter.

The area under a continuous distribution, that lies above and below two points. P(outside) = 1 - P(between) = 1 - (CDF($x₂) - CDF($x₁))

public static outside ( number $x₁, number $x₂, $params ) : number
$x₁	number	Lower bound
$x₂	number	Upper bound
$params		Remaining parameters for each distribution
return	number

Produce a random number with a particular distribution

public static rand ( $params )